**Unit 3 - Applications of Differentiation**

12.10.19 5.4 The derivative of Exponential Functions Pg. 358 #5, 13, 15, 41, 45, 49, 53, 57, 66, 69

12.9.19 5.3 Inverse Functions Pg. 349 #75, 76, 81, 85, 101-104

12.6.19 5.1 The Natural Logarithmic Function Pg. 331 #7-10, 19, 23, 27, 31, 35, 47, 49-52, 57, 59,65, 69, 75, 77, 88, 93, 101

12.5.19 8.7 L'Hopital's Rule Pg. 576 #7, 8, 11-14, 21-22, 25-27, 39

12.3.19 3.9 Differentials and Local Linearity Pg. 240 #3, 21-31 odd, 39, 43-48

12.2.19 Related Rates vs. Optimization

11.25.19 Connecting a function, its derivative and its second derivative

11.22.19 3.7 Optimization Problems Pg. 223 #5, 7, 13, 15, 17, 21, 29, 33, 39, 40, 42a, 49, 54

11.19.19 3.2 The Mean Value Theorem Pg. 176 #13, 15, 17, 18, 21, 23, 37, 39, 41, 43, 46, 59, 64, 77-80

11.18.19 Review Pg. 242 (2 problems from 3-6; 3 from 7-20; 2 each from 21-32,

33-42, 47-60, 66, 67, 73

11.15.19 3.6 Curve Sketching

**P**g. 215 # 7, 13, 17, 19, 21, 31, 33, 41, 49-50, 61-62, 71-72

11.12.19 3.4 The second Derivative Test pg. 195 #9, 14, 25, 35, 43, 45, 61-64, 67, 73, 91-94

11.07.19 3.1 and 3.3 Review (in class handout) Pg. 169 - 12, 19, 33, 41, 45 and Pg. 186 - 19, 33, 35, 45, 47

11.05.19 3.3 The first Derivative Test Pg. 186 -

**21, 22, 27, 34, 37, 43, 44, 51, 61-68, 71-76**

11.04.19 3.1 Extrema on an Interval Pg. 169 - 11, 15, 21, 25, 36, 42, 54, 57-60, 63, 65-69

Our discussion about applications of differentiation includes the following topics: Rolle's Theorem and the Mean Value Theorem, Determining Intervals on which a function is increasing or decreasing, Absolute vs. Relative Extrema, critical points, concavity of functions over their domain, the Second Derivative Test, sketching graphs, connecting functions with their first and second derivative, Optimization Problems, Behavior of Implicit Relations, and the derivatives of inverse functions

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